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In this work, different previously unexplored features are investigated for the radiation performance of linear phased arrays based on printed-circuit leaky-wave antennas for microwave and millimeter-wave applications. By means of a rigorous modal analysis in the unit cell based on the spectral-domain approach, we have considered the beam-scanning properties of microstrip leaky-wave arrays in terms of spatial harmonics, as a function of both the phase shift and the spacing between the radiating microstrip lines. We have thus found and interpreted in a consistent way various original characteristics, such as transition regions between leaky-wave and surface-wave regimes, and the occurrence of spurious radiation (grating lobes) in largely spaced arrays related to the presence of new, additional complex improper modes. Numerical full-wave simulations of the radiation patterns for realistic configurations of microstrip arrays confirm the theoretical predictions made on the basis of the modal properties of the involved leaky waves.